Gyroscopes are currently used in a number of military and civilian applications. One common application involves using gyroscopes, known as control moment gyroscopes (CMGs), to control the attitude (or orientation) of a spacecraft, satellite, or another agile vehicle. A CMG comprises a spinning rotor and one or more motorized gimbals, which are used to rotate the rotor (e.g., gimballing), which in turn alters the direction of the angular momentum vector of the rotor. This change in angular momentum produces a reactionary torque which causes the spacecraft to rotate to the desired attitude or orientation. Attitude control systems (ACSs) and other spacecraft orienting applications often utilize a momentum control system (MCS) that includes at least three single-gimbal CMGs, also known as a CMG array.
Hardware limitations of the CMGs limit the amount of momentum that may be transferred and/or stored by the individual CMGs. Also, particular arrangements of the CMGs in the CMG array, known as singularities, limit the ability of the CMG array to produce torque in certain directions, thereby limiting the ability of the ACS to reorient the vehicle in some directions. Therefore, one or more control schemes, also known as steering control laws, are utilized by the MCS to determine how the individual CMGs should be rotated to produce a desired overall torque (or a commanded torque) without causing singularities or saturation in the CMG array. Often, the steering control law(s) impose a limit on the amount of momentum that may be stored and/or transferred by the CMG array. The momentum limit is a non-linear and complex function of the direction of the spacecraft's angular momentum, the angular position of the gimbals (or gimbal angles) for the individual CMGs of the CMG array, and the steering control law(s) being utilized with the CMG array. In this regard, in three-dimensional space, the momentum limits imposed by the steering control law(s) may be represented as an irregular polyhedron comprising the set of allowable momentum vectors in the various momentum directions.
Because the momentum limit imposed by the steering control law(s) is complex and non-linear, most prior art attitude control systems utilize a self-imposed momentum limit that is confined by the momentum limits imposed by the steering control law(s). In this regard, in three-dimensional space, the self-imposed momentum limits may be represented as a sphere inscribed within the irregular polyhedron corresponding to the momentum limits imposed by the steering control law(s). In some applications, it is desirable to be able to reorient a vehicle as quickly as possible. However, the prior art systems conservatively limit the momentum of the CMG array and fail to maximize the momentum capabilities achievable under the steering control law(s). Thus, although the CMG array is capable of providing additional momentum (corresponding to the volume between the outer surfaces of the irregular polyhedron and the sphere inscribed within the polyhedron in three-dimensional space) that would allow the vehicle to be reoriented more quickly, the available momentum of the CMG array is not fully utilized by the prior art.